29. Noting that the real part of Equation 19 is identical to the 

 summation term in Equation 24 and that the imaginary part of Equation 19 is 

 identical to minus the summation term in Equation 26, it is clear that 



(31) 



and 



k = 2, 3, 



(32) 



Similarly, 



\i 



i ^yi - N ^1 



(33) 



and 



V - i B 



— — Y 



yk jg -^k 



k = 2, 3, 



(34) 



for time series y^^ . These relationships show how the Fourier series 

 coefficients and Fourier transform components are related. 



30. It is also useful to note that the Fourier series of Equation 21 

 can be written as 



N/2 



Xn = ^ C^k COS 



k=l 



27r(k - l)(n - 1) 



N 



n = 1, 2 



(35) 



where the cosine and sine amplitudes A^^ and B^^^ , respectively, of 

 Equation 21 are related to the modulus C^^ and phase (p^^ of Equation 35 by 



A„^ = C^v cos 



(36) 



and 



= C„t sin 



(37) 



0^1, — A„i, + 



(38) 



and 



16 



